# Sum of pure errors

We know that in a simple linear regression model that the sum of all the residuals is 0 but why is it that the sum of all the pure errors is also 0? Is there a relation between them?

• Could you explain what you mean by "pure errors"? I ask because the natural interpretation would be that in a model $Y=X\beta + \varepsilon$ the random term $\varepsilon$ would be the "pure error," but obviously neither that variable nor a sum of them (assuming they are independent, as always) would equal zero. – whuber Apr 18 at 13:21
• Do you mean a sum of pure errors, $\sum_i(y_i-\hat{y}_i)$, in contrast to the sum of squared errors, $\sum_i(y_i-\hat{y}_i)^2$? – Dave Apr 18 at 15:54